Elbow grease and Dawn dishwashing liquid. Grab a dish sponge with a scrubber!
the Mr. Clean magic erasers work well on glass, I would not use them on plastic or acrylic doors as it may scratch.
Bartenders Keeper with some water will clean just about anything, just water it down and test first to make sure it doesn't scratch the glass
Vinegar is good if you can somehow let it soak on there, but guess you can not since it will run off the door.
If its textured glass like the kind you can't see through totally Then it will always come back.
This will sound odd, but, try some muriatic acid first. It is used in swimming pools to help maintain Ph balance. MUST use plenty of ventilation & gloves!!!!!..... Mix approx. 50/50 with water & spray on & let it sit for a few minutes. Rinse well. That should take at least some of it off. If not all of it is gone, try a spot with some Barkeepers Friend. it can be used on many things including ceramic tiles, so it might be what you need to do the job.
If you get it all cleaned, use a squeegee after every shower to keep the water from drying on the glass.
There is a recipe for a cleaner which is vinegar and Dawn dishwashing detergent. It works great. I just do not have the recipe here (south for winter).
Vinegar, it won't hurt the surrounding areas. Vinegar is also good disinfectant.